Title : Further Results for Goodness-of-Fit Statistics with Unknown Parameters.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS

Personal Author(s) : Stephens,M. A.

Report Date : 04 OCT 1971

Pagination or Media Count : 36

Abstract : The report revises and extends the report Asymptotic results for goodness-of-fit statistics when parameters must be estimated (Stephens, 1970); new theoretical and numerical results are given. In particular the weights are calculated when asymptotic distributions of W squared, U squared, and A (statistics associated with Cramer-von Mises, Watson and Anderson-Darling) are expressed as weighted sums of chi square sub 1 variables. These lead ultimately to the provision of percentage points for W squared, U squared, and A in tests for normality and exponentiality, when parameters must be estimated. The previous report gave only means and variances of asymptotic distributions; some of these are repeated for completeness. (Author)